Method and Apparatus for Determining Joint Randomness

ABSTRACT

A method and apparatus for performing Joint Randomness Not Shared by Others (JRNSO) is disclosed. In one embodiment, JRNSO is determined in Frequency Division Duplex (FDD) using a baseband signal loop back and private pilots. In another embodiment, JRNSO is determined in Time Division Duplex (TDD) using a baseband signal loop back and combinations of private pilots, private gain functions and Kalman filtering directional processing. In one example, the FDD and TDD JRSNO embodiments are performed in Single-Input-Single-Output (SISO) and Single-Input-Multiple-Output (SIMO) communications. In other examples, the FDD and TDD embodiments are performed in Multiple-Input-Multiple-Output (MIMO) and Multiple-Input-Single-Output (MISO) communications. JRNSO is determined by reducing MIMO and MISO communications to SISO or SIMO communications. JRNSO is also determined using determinants of MIMO channel products. Channel restrictions are removed by exploiting symmetric properties of matrix products.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of, and claims priority to, U.S.patent application Ser. No. 12/106,926, filed on Apr. 21, 2008, whichclaims the benefit of U.S. Provisional Patent Application Nos.60/912,749, filed on Apr. 19, 2007; 60/941,978, filed on Jun. 5, 2007;60/943,665, filed on Jun. 13, 2007; 60/976,686 filed on Oct. 1, 2007;and 60/981,249 filed on Oct. 19, 2007, all of which are incorporatedherein by reference as if fully set forth.

TECHNICAL FIELD

This application is related to wireless communications.

BACKGROUND

Developments in cryptographic theory demonstrate how informationtheoretic secrecy can be generated from sources of joint randomnessunder the assumption that the potential attacker/eavesdropper does notsignificantly share the same source of randomness. These developmentsmay be particularly well-suited for use in secrecy generation inwireless communication systems due to the nature of the wirelesscommunication medium.

In order to communicate secretly, information-theoretic security couldbe used to protect communications between two terminuses, from beingdiscovered by an attacker entity. Most wireless channels have aconstantly changing physical property, which provides a lot ofrandomness on the terminus's channel observations. This is called thisJoint Randomness Not Shared by Others (JRNSO) and is the subject of U.S.patent application Ser. No. 11/339,958.

In the prior art, JRNSO typically relies on two terminuses observingessentially the same Channel Impulse Response (CIR), a situationinherent to Time Division Duplex (TDD) where there is one reciprocalchannel. Many communication systems however utilize Frequency DivisionDuplex (FDD), where two terminuses typically do not observe essentiallythe same channel impulse response due to the fact the signaltransmission in each direction is on a significantly different channelfrequency. Further, there is a need to make JRNSO based encryption inTDD applications more robust, and to expand JRNSO to environments whichdo not naturally produce sufficient JRNSO information. This could be dueto the channel not being as close to true reciprocity as required forthe application. These techniques are applicable toSingle-Input-Single-Output (SISO) and Single-Input-Multiple-Output(SIMO) systems. Finally, there is a need to extend JRNSO to moresophisticated communication systems which usemultiple-input-multiple-output (MIMO) or multiple-input-single-output(MISO) antenna arrays.

SUMMARY

Methods and apparatus for determining JRNSO are disclosed. In oneembodiment, JRNSO is determined in FDD using a baseband signal loop backand private pilots. In another embodiment, JRNSO is determined in TDDusing a baseband signal loop back and combinations of private pilots,private gain functions and optionally Kalman filtering or similar timedirectional processing. In one example, the FDD and TDD JRSNOembodiments are performed in SISO and SIMO communication steps. In otherexamples, the FDD and TDD embodiments are performed in MIMOcommunications. JRNSO is determined by reducing MIMO and MISOcommunications to SISO or SIMO communications. In still otherembodiments channel measurement signaling restrictions are removed byexploiting symmetric properties of matrix products, such asdeterminants.

BRIEF DESCRIPTION OF THE DRAWINGS

A more detailed understanding may be had from the following description,given by way of example in conjunction with the accompanying drawingswherein:

FIG. 1 shows an example of a block diagram of a wireless communicationsystem configured to use JRNSO;

FIG. 2 shows an example of a JRNSO procedure in FDD using a loop backapproach and public pilots;

FIG. 3 shows an example of a JRNSO procedure in FDD using a loop backapproach and private pilots;

FIG. 4 shows an example of a JRNSO signal process in FDD as a functionof time;

FIG. 5 shows an example of a JRNSO channel modification process in FDD;

FIG. 6 shows an example of a JRNSO channel modification process in FDDas a function of time;

FIG. 7 shows an example of JRNSO channel utilization in FDD as afunction of time;

FIG. 8 shows an example of JRNSO channel utilization usingsimplification assumptions in FDD as a function of time;

FIG. 9 shows an example of a JRNSO signal process in FDD using randomtime positioning of a loop back signal;

FIG. 10 shows an example of the relationship of signal to noise ratio toan error rate;

FIG. 11 shows an example of a JRNSO procedure in TDD using a loop backapproach with public pilots and private gain functions;

FIG. 12 shows an example of a JRNSO signal process in TDD as a functionof time;

FIG. 13 shows an example of a JRNSO signal process in TDD using pairedlike transmissions;

FIG. 14 shows an example of a JRNSO signal process during a pilot periodin TDD;

FIG. 15 shows an example of a JRNSO signal process during a data periodin TDD;

FIG. 16 shows an example of a Kalman filter;

FIG. 17 shows an example of Kalman filtering directional processing;

FIG. 18 shows an example of a JRNSO signal process in MIMO;

FIG. 19 shows an example of a JRNSO signal process in MIMO;

FIG. 20 shows an example of derivable channel products in MIMO;

FIG. 21 shows an example of JRNSO measurements as a function of time;

FIG. 22 is shows an example of a JRNSO procedure in MIMO using a loopback approach with public pilots and private gain functions;

FIG. 23 shows an example of derivable products using square matrixtransmission sequences in FDD; and

FIG. 24 shows an example of a JRNSO procedure in FDD symmetric MIMO.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

When referred to hereafter, the terminology “wireless transmit/receiveunit (WTRU)” includes but is not limited to a user equipment (UE), amobile station, a fixed or mobile subscriber unit, a pager, a cellulartelephone, a personal digital assistant (PDA), a computer, or any othertype of user device capable of operating in a wireless environment. Whenreferred to hereafter, the terminology “base station” includes but isnot limited to a Node-B, a site controller, an access point (AP), or anyother type of interfacing device capable of operating in a wirelessenvironment.

FIG. 1 shows an example of a block diagram of a wireless communicationsystem 100 configured to use JRNSO. A Radio Frequency (RF) communicationchannel set 105 between wireless transmit/receive units (WTRUs), hereAlice 110 and Bob 120, is shown. Eve 130 is an attacker entity who maymonitor the RF communication channel set 105 between Alice 110 and Bob120. Let Alice 110 and Bob 120 be two wireless terminuses, whichcommunicate with each other on the same frequency in a wirelessenvironment. Due to the channel reciprocity, if these two terminusesobserve their mutual channels 105 at approximately the same time, theirobservations will be very similar to each other. A third terminal, Eve130 is shown located more than a wavelength away from Alice 110 and Bob120, and the channel observations 115 and 125 by Eve 130 are almostcertainly independent from the channel-specific observations by Alice110 or Bob 120.

Therefore, Alice 110 and Bob 120 could generate a common secret keybetween them based on their channel observations. In generating such akey, Alice 110 and Bob 120 may need to communicate with each other usingone of the loop back signaling procedures described below.

FIG. 2 shows an example of a JRNSO procedure performed by the system ofFIG. 1. In this example, a loop back approach is used in a FrequencyDivision Duplex (FDD) mode using public pilots. A solid line indicatesAlice's 110 loop back process. A dashed line indicates Bob's 120 loopback process.

Alice 110 initiates her loop back process by transmitting a public pilotp 200 to Bob 120 over channel G_(AB) 205, creating a resulting signalG_(AB)p 210. Bob 120 receives the signal G_(AB)p 210 and translates thesignal to baseband. Bob 120 does not otherwise process the signal. Bob120 sends the signal back to Alice 110 over a channel with a differentfrequency G_(BA) 230, which creates a resulting signal G_(BA)G_(AB)p235. Alice 110 receives the looped back signal G_(BA)G_(AB)p at 240completing her loop back process.

Bob 120 initiates his loop back process by transmitting a public pilot p245 to Alice 110 over channel G_(BA) 230, creating a resulting signalG_(BA)p 250. Alice 110 receives the signal G_(BA)p 250 and translatesthe signal to baseband. Alice 110 does not otherwise process the signal.Alice 110 sends the signal back to Bob 120 over a channel with adifferent frequency G_(AB) 205, which creates a resulting signalG_(AB)G_(BA)p 260. Bob 120 receives the looped back signal G_(AB)G_(BA)p260 at 265 completing his loop back process.

During the communication, Eve 130 may monitor Bob's 120 transmittedsignals over channel G_(BE) 270, which will allow Eve 130 to observe theresulting signals G_(BE)G_(AB)p 280 and G_(BE)p 290. Although notdepicted in FIG. 2, Eve 130 may also monitor Alice's 110 transmittedsignals over channel G_(AE), which will allow Eve 130 to observe theresulting signals G_(AE)p and G_(AE)G_(BA)p.

When, the loop back process has been completed for Alice 110 and Bob120, then Alice 110 has observed at 240 G_(BA)G_(AB)p 235 and G_(BA)p250; and Bob 120 has observed at 265 G_(AB)p 210 and G_(AB)G_(BA)p 260.Alice 110 processes her two received signals to determine G_(BA) andG_(AB). Similarly, Bob 120 processes his two received signals todetermine G_(AB) and G_(BA). Eve 130 has observed G_(BE)p,G_(BE)G_(AB)p, G_(AE)p and G_(AE)G_(BA)p. Eve 130 knows the publicpilots, so she can determine G_(BE), G_(BE)G_(AB), G_(AE) andG_(AE)G_(BA) Given these four, Eve 130 can perform further calculationsand determine G_(AB) and G_(BA). This shows that a basic FDD enablementof channel information sharing between Alice 110 and Bob 120 whilepossible is not secure against Eve 130 when using public pilots.

FIG. 3 is an example of a JRNSO procedure performed by the system ofFIG. 1 which is secure against Eve 130. In this example, a loop backapproach is used in a Frequency Division Duplex (FDD) mode using privatepilots known only to the respective initial sender, Alice 110 or Bob120. While Alice's 110 loop back cycle is discussed first, the JRNSOprocess is most efficient when Alice and Bob initiate their respectiveloop back cycles simultaneously.

Alice 110 initiates her loop back process by transmitting a privatepilot p_(A) 300 to Bob 120 over channel G_(AB) 205, creating a resultingsignal G_(AB)p_(A) 310. Bob 120 receives the signal G_(AB)p_(A) 310 andtranslates the signal to baseband. Bob 120 does not otherwise processthe signal or attempt to exploit it. Bob 120 sends the signal back toAlice 110 over a channel with a different frequency G_(BA) 230, whichcreates a resulting signal G_(BA)G_(AB)p_(A) 320. Alice 110 receives thelooped back signal G_(BA)G_(AB)p_(A) at 335 completing her loop backprocess.

Bob 120 initiates his loop back process at nearly the same time as Aliceby transmitting a private pilot p_(B) 340 to Alice 110 over channelG_(BA) 230, creating a resulting signal G_(BA)p_(B) 345. Alice 110receives the signal G_(BA)p_(B) 250 at 335 and translates the signal tobaseband. Alice 110 does not otherwise process the signal or attempt toexploit it. Alice 110 sends the signal G_(BA)p_(B) 345 back to Bob 120over a channel with a different frequency G_(AB) 205, which creates aresulting signal G_(AB)G_(BA) p_(B) 350. Bob 120 receives the loopbacked signal at 355 completing his loop back process.

Note that while from a general standpoint Alice 110 and Bob 120 need notbe simultaneously performing their measurements, it is advisable fromthe standpoint of most likely having the signal measurements occur withcorrelated channel effects.

During the communication between Alice 110 and Bob 120, Eve 130 maymonitor Alice's 110 transmitted signals over channel G_(AE) 360 andBob's 120 transmitted signals over channel G_(BE) 270. If Eve 130 ismonitoring Alice's 110 transmissions, Eve 130 observes the signalsG_(AE)p_(A) 370 and G_(AE)G_(BA)p_(B) 389. If Eve 130 is monitoringBob's 120 transmissions, Eve observes the signals G_(BE)p_(B) 385 andG_(BE)G_(AB)p_(A) 380.

After the loop back process has been completed for Alice 110 and Bob120, Alice 110 has observed at 335 G_(BA)G_(AB)p_(A) 320 and G_(BA)p_(B)345; and Bob 120 has observed at 355 G_(AB)p_(A) 310 andG_(AB)G_(BA)p_(B) 350. Alice however is not able to process G_(BA)p_(B)345 since she does not know p_(B). Likewise Bob can not determineG_(AB)p_(A) 315, because Alice 110 and Bob 120 respectively, know theprivate pilots they used, Alice 110 can calculate the channel matrixproduct G_(BA)G_(AB) 391, and Bob 120 can calculate the channel matrixproduct G_(AB)G_(BA) 393. In this example, Alice 110 and Bob 120 usesingle-input-single-output (SISO) signaling so that the channel matricesare Rank 1. Therefore, the channel matrices degenerate to a single valueand are commutative (e.g. G_(AB)G_(BA) 393=G_(BA)G_(AB) 391). Alice 110and Bob 120, can then determine essentially identical CIRs.

Due to the private nature of the pilots in this example, Eve 130 isunable to separate the channel induced scaling, skewing, and rotationaleffects from the settings inherent to the private pilots. From thestandpoint of the equations, the pilots can not be separated from thechannel matrices. Therefore, Eve 130 is unable to determine G_(BA)G_(AB)391.

FIG. 4 is an example of the channel utilization time constraints of thesignaling process depicted in FIG. 3. In this example, Alice 110 and Bob120 use private pilots during the JRNSO determination period and publicpilots during the data transmission periods. There are two channels: anAlice to Bob channel G_(AB) 405 on a certain frequency, and a Bob toAlice channel G_(BA) 410 on a different frequency. Data transmissionperiods are depicted at 420. A JRNSO determination period is depicted at425. Time delays (t_(c) _(—) _(delay)) are depicted at 430 and occurbetween the data periods 420 and the JRNSO period tJRNSO 425. There is apublic pilot p which Alice 110 and Bob 120 use during data transmissionperiods 420. There is a private pilot p_(A), known only to Alice 110,which Alice 110 transmits during the JRNSO period 425 to initiate herloop back process. There is a private pilot p_(B), known only to Bob120, which Bob 120 transmits during the JRNSO period 425 to initiate hisloop back process.

In the example of FIG. 4, channel transforms are shown as a function oftime. Time t increases from left to right. First, there is a data period420. Then, there is a tc_delay 430 while Alice 110 and Bob 120 switch toa JRSNO mode. Then, Alice 110 and Bob 120 start the JRSNO process. Alice110 initiates her loop back cycle by sending a private pilot p_(A) overchannel G_(AB) to Bob 120, resulting in a signal G_(AB)(t_(j))p_(A) 435.Bob 120 translates the signal to baseband but does not otherwise processthe signal. Bob 120 sends the return signal back to Alice 110. Alice 110receives and processes the looped back signal.

At the same time that Alice 110 initiates her loop back process, Bob 120initiates his loop back process by sending a private pilot p_(B) overchannel G_(BA) to Alice 110, resulting in a signal G_(BA)(t_(j))p_(B)445. Alice 110 translates the signal to baseband but does not otherwiseprocess the signal. Alice 110 sends the return signal back to Bob 120.Then, Bob 120 receives and processes the looped back signal.

When the JRNSO determination period is complete, there is a time delay430 as Alice 110 and Bob 120 switch to a non-JRNSO mode.

As shown in the example of FIG. 4, and to ensure security from Eve 130,the time delay between the data periods and the JRNSO period exceeds themaximum coherence time of either channel tG_(AB) and tG_(BA), wheretc_delay>max(tG_(AB), tG_(BA)). As further shown in the example of FIG.4, the JRNSO period is less than the minimum coherence time of eitherchannel, where t_(JRNSO)<min(tG_(AB),tG_(BA)). The delay tc_delay isnecessary to prevent Eve 130 from determining essentially the samechannel parameters that exist during the JRNSO time period from the dataperiod. The maximum observation time t_(JRNSO) is necessary to assumethat Alice 110 and Bob 120 measure essentially the same channel effectsduring the measurement period.

Some applications, for example e-mail, file transfer, buffered streamingaudio or video, are tolerant of a long tc_delay. Other applications, forexample audio conversations, can not tolerate a long tc_delay, and it isnecessary to reduce the tc_delay. The tc_delay also has an impact on theoverall utilization of the radio channels. It is therefore desirable toreduce its duration to improve the utilization of the channel for datatransfer and JRNSO purposes.

In one embodiment, the tc_delay 430 is reduced by using special pilotconstellations during the data periods. The pilot constellations, whichare functions of the JRNSO determinations, are known to both Alice 110and Bob 120, but not to Eve 130. Therefore, Alice 110 and Bob 120, whoknow more than Eve 130, can calculate the channel transforms. Eve 130,however, can only calculate the channel transforms if Eve 130synchronizes all four data streams to the same instant.

In another embodiment, the tc_delay 430 is reduced by modifying thechannel transforms between the data periods and JRNSO periods. FIG. 5 isan example of a JRNSO procedure performed by the system of FIG. 1, hereshowing a general overall channel modification system in FDD mode. Inthis example, the channel transforms between Alice 110, Bob 120 and Eve130 are modified so that the channel transforms during the JRNSO periodsdiffer from the channel transforms during the data periods.

G_(AB), G_(BA), G_(AE), G_(BE) are the channel transforms between Alice110, Bob 120 and Eve 130 under normal conditions.

J_(AB), J_(BA), J_(AE), J_(BE) are the channel transforms between Alice110, Bob 120 and Eve 130 during JRNSO periods.

D_(AB), D_(BA), D_(AE), D_(BE) are the channel transforms between Alice110, Bob 120 and Eve 130 during data periods.

An example of a general form channel transform is depicted at 500, wherethe resulting channel matrix is G_(XY)G_(X)p_(X). An example of achannel transform during data periods is depicted at 503, where theresulting channel matrix G_(XY)D_(X)p=D_(XY)p. An example of a channeltransform during JRNSO periods is depicted at 506, where the channelmatrix is G_(XY)J_(X)P_(X)=J_(XY)p_(X).

In this example, Alice 110 and Bob 120 apply respective functions G_(A)and G_(B) each time they transmit a signal.

G_(A) is any function applied by Alice 110 that modifies the channeltransform so that the channel transform during JRNSO periods differsfrom the channel transform during data periods.

G_(B) is any function applied by Bob 120 that modifies the channeltransform so that the channel transform during JRNSO periods differsfrom the channel transform during data periods.

G_(A)=J_(A1)=a function applied by Alice during her loop back processduring a JRNSO period.

G_(A)=J_(A2)=a function applied by Alice during Bob's loop back processduring a JRNSO period.

G_(B)=J_(B1)=a function applied by Bob during his loop back processduring a JRNSO period.

G_(B)=J_(B2)=a function applied by Bob during Alice's loop back processduring a JRNSO period.

G_(A)=D_(A)=a function applied by Alice during a data period.

G_(B)=D_(B)=a function applied by Bob during a data period.

Alice 110 initiates her loop back process by applying a function G_(A)509 to a private pilot p_(A) 512 and transmitting the signal p_(A) 515to Bob 120 over channel G_(AB) 205, creating a resulting signalG_(AB)p_(A) 518. Bob 120 receives the signal G_(AB)p_(A) 518 andtranslates the signal to baseband. Bob applies a function G_(B) 521 tothe signal and sends the signal G_(AB)p_(A) 524 back to Alice 110 over achannel with a different frequency G_(BA) 230, creating signalG_(BA)G_(AB)p_(A) 527. Alice 110 receives the looped back signalG_(BA)G_(AB)p_(A) 527 completing her JRNSO loop back process.

Bob 120 initiates his loop back process when he applies a function G_(B)521 to a private pilot p_(B) 530 and sends the signal to Alice 110 overchannel G_(BA) 230, creating a resulting signal G_(BA)p_(B) 533. Alice110 receives the signal G_(BA)p_(B) 533 and translates the signal tobaseband. Alice 110 applies a function G_(A) 509 and sends the signalG_(BA)p_(B) 536 back to Bob 120 over a channel with a differentfrequency G_(AB) 205, creating a resulting signal G_(AB)G_(BA)p_(B) 539.Bob 120 receives the looped back signal G_(AB)G_(BA)p completing hisloop back process.

After the loop back process has been completed for Alice 110 and Bob120, then Alice 110 has observed G_(BA)G_(AB)p_(A) 527 and G_(BA)p_(B)533; and Bob 120 has observed G_(AB)p_(A) 518 and G_(AB)G_(BA)p_(B) 539.While Eve 130 has observed different values during the data periods andJRNSO periods, the functions G_(A) and G_(B) effects are indivisiblefrom the overall channel transform. Therefore, Alice 110 and Bob 120,who know their private pilots, are able to calculate their channeltransforms. However, Eve 130, is only able to calculate the channeltransforms if she synchronizes the four sampling streams to the samecorresponding instant. By using different channel modifying transforms,Eve 130 does not observe the same fluctuations in the channels for bothdata and JRNSO signaling periods. Eve 130 therefore would not determinethe same channel information as Alice 110 and Bob 120 even though theactual channel had not significantly deviated during the two timeperiods. Eve 130 could get around this approach by synchronizing theactual samples from the different measurements and processing thesemeasurements to remove the effects of the private gain functions beforestatistically determining the channel effect matrices.

In the channel modification example of FIG. 5, the functions G_(A) andG_(B) may be applied before amplification, during amplification or afteramplification.

FIG. 6 shows an example of a time function diagram where the tc_delayhas been minimized as a result of the channel modification process inFIG. 5. A data period 600 is depicted where Alice 110 and Bob 120transmit signals using a public pilot p 605. A JRNSO period 610 isdepicted where Alice 110 and Bob 120 transmit signals using privatepilots 615. Delays between the data periods and JRNSO period aredepicted at 620, where the delays may be caused by channel switch over,synchronization or settling. The JRNSO period is less than the minimumchannel coherence time 625 of either of the channels.

FIG. 7 shows an example of the channel modification process in FIG. 5where the channel conditions and private pilots are varied according towhether the period is a JRNSO period or a data period. There are twochannels depicted: an Alice to Bob channel 700 on one frequency and aBob to Alice channel 705 on another frequency. There is a JRNSO timeperiod (k) 710. There is a data time period (k−1) 715 which precedes theJRNSO time period (k) 710. There is a data time period (k+1) 720 whichoccurs subsequent to the JRNSO time period (k) 710.

During the preceding data time period (k−1) 715, Alice 110 and Bob 120transmit signals D_(AB)(k−1)p 740 and D_(BA)(k−1)p 745, respectively,where p is a public pilot. During the JRNSO time period (k) 710, Alice110 transmits signals J_(AB)(k)p_(A)(k) 750 andJ_(AB)(k)J_(BA)(k)p_(B)(k) 755, and Bob 120 transmits signalsJ_(BA)(k)p_(B)(k) 760 and J_(BA)(k)J_(AB)(k)p_(A)(k) 765, where p_(A)and p_(B) are private pilots known only to Alice 110 and Bob 120,respectively. During the subsequent data period (k+1) 720, Alice 110 andBob 120 transmit signals D_(AB)(k+1)p 770 and D_(BA)(k+1)p 775,respectively, where p is a public pilot.

In the example of FIG. 7, the channel conditions are adjusted accordingto a given situation. For example, the channel values may be maintainedat a relatively constant level during each time period to provide robuststatistical analysis capabilities. Alternatively, the channel values maybe varied within each time period to prevent Eve 130 from obtaining moreinformation than Alice 110 and Bob 120 require for performing theirJRNSO determinations. Another alternative is to use the basic functionsto pre-process signals or to mitigate known channel variations.

FIG. 8 shows an example of the signaling process in FIG. 5 where channelconditions are varied according to whether the period is a JRNSO periodor a data period. In this example, data samples are processed prior tostatistical analysis and the end to end channel transforms are set to aperfect channel condition identity. Signals are depicted as functions ofconditions which vary according to the channel utilization; where (k)800 is the condition during the JRNSO period 805, (k−1) 810 is thecondition during the data period 815 which precedes the JRNSO period805, and (k+1) 818 is the condition during the data period 820 whichfollows the JRNSO period 805. Delays between the data periods 815, 820and JRNSO period 805 are depicted at 825.

During the data period 815 which precedes the JRNSO period 805, Alice110 and Bob 120 transmit signals G_(A)(k−1)p 840 and G_(B)(k−1)p 845,respectively, where p is a public pilot. During the JRNSO period 805,Alice 110 transmits signals G_(A)(k)p_(A)(k) 850 andG_(A)(k)G_(B)(k)p_(B)(k) 855, and Bob 120 transmit signalsG_(B)(k)p_(B)(k) 860 and G_(B)(k)G_(A)(k)p_(A)(k) 865, where p_(A) andp_(B) are private pilots known only to Alice 110 and Bob 120,respectively. During the data period 820 which follows the JRNSO period805, Alice 110 and Bob 120 transmit signals G_(A)(k+1)p 870 andG_(B)(k+1)p 875, respectively, where p is a public pilot.

If Alice 110 and Bob 120 consistently transmit their private pilotsconcurrent to the transmission start up, and the signal to noise ratiois robust, then a sophisticated Eve 130 may be able to detect thebeginning of the sequences and properly align the samples.

FIG. 9 shows an example of the signaling process in FIG. 5 where loopback signals are transmitted according to random time positioning. Inthis example, the boundaries 900 between the data periods 905 and JRNSOperiod 910 are masked by using a loop back function. The loop backfunction introduces a random delay between the time a pilot is receivedand the time that pilot is transmitted. The random delay is created byintroducing false feed back data, referred to here as a falsemodulation. The false modulation may be introduced before or aftercompletion of Alice's or Bob's respective loop back. If the JRNSOdetermination period is less than the minimum channel coherence time ofeither channel, then Eve's ability to calculate the channel transformsis made computationally intensive, although not theoreticallyimpossible.

In this example:

b_(A)=a false modulation inserted by Alice 110 before completion of herloop back process;

a_(A)=a false modulation inserted by Alice 110 after completion of herloop back process;

b_(B)=a false modulation inserted by Bob 120 before completion of hisloop back process; and

a_(B)=a false modulation inserted by Bob 120 after completion of hisloop back process.

As shown in FIG. 9, Alice 110 and Bob 120 may initiate and completetheir loop back processes at the same time. In one embodiment, Alice 110initiates her loop back process by transmitting a signal J_(AB)p_(A) 915to Bob 120, and Bob 120 initiates his loop back process by transmittinga signal J_(BA)p_(B) 935 to Alice 110. Next, Alice 110 introduces afalse modulation b_(A) 920 and Bob 120 introduces a false modulationb_(B) 940. As shown at 938, Alice 110 and Bob 120 may introduce thefalse modulations before or after they transmit their respective returnsignals. Next, Alice 110 receives her looped back signalJ_(BA)J_(AB)p_(A) 925 completing her loop back process, and Bob 120receives his looped back signal J_(AB)J_(BA)p_(B) 945 completing hisloop back process.

In another embodiment, Alice 110 initiates her loop back process bytransmitting a signal J_(AB)p_(A) 915 to Bob 120, and Bob 120 initiateshis loop back process by transmitting a signal J_(BA)p_(B) 935 to Alice110. Next, Alice 110 receives her looped back signal J_(BA)J_(AB)p_(A)925 and introduces a false modulation a_(A) 930, and Bob 120 receiveshis looped back signal J_(AB)J_(BA)p_(B) 945 and introduces a falsemodulation a_(B) 950. As shown at 948, the loop back process is notcomplete until after the false modulations a_(A) 930 and a_(B) 950 havebeen introduced.

The above two embodiments may be expanded where Alice 110 and Bob 120introduce false modulations at random times during the JRNSO periodeither at the start, end, or interleaved with the actual measurementsignaling. If the JRNSO period 910 is less than the minimum coherencetime of the channels G_(AB) and G_(BA), then Eve 130, who cannotidentify a false modulation from a true JRNSO to data period boundary,cannot synchronize the four data streams and align the samples.

FIG. 10 is an example of a graph depicting the error rate to signal tonoise ratio for the channel coder used to exchange information betweenAlice 110 and Bob 120, to consolidate their similar channel impulseobservations into one common observation. This encoding technique isused to exploit Eve's 130 weaker knowledge of the channel between Alice110 and Bob 120 which translates into an effective weaker signal tonoise ratio of the channels observed by Eve 130 of either Alice 110 orBob 120. This is exploited to exchange information between Alice 110 andBob 120 and to consolidate the channel observations without revealingthe true channel observations to Eve 130. The error rate 1000 (y-axis)is represented as a function 1005 of the signal to noise ratio 1010(x-axis). As the signal to noise ratio 1010 increases, the error rate1000 remains relatively constant and then sharply decreases 1020. Asdepicted, Alice's 110 and Bob's 120 signal to noise ratio 1025 is to theright of the knee of curve 1005 exceeds Eve's 130 signal to noise ratio1030 which is to the left of the knee of curve 1005. Because the errorrate decreases as the signal to noise ratio increases, Alice's 110 andBob's 120 error rate 1035 is significantly less than Eve's 130 errorrate 1040.

To ensure that Eve 130 has a higher error rate, Alice 110 and Bob 120monitor and control their respective SNR conditions with the goal beingto maintain their own respective SNR conditions to lie at the knee ofcurve 1005 as depicted in FIG. 10.

The channel observation by Eve 130 may be controlled by any combinationof adjusting the channel distortion controls or adding noise into thedata streams transmitted by Alice 110 or Bob 120. Pseudo-noise may beadded into the data streams during signal origination, and during theloop back process. Eve's 130 channel observation may be controlled byAlice 110 or Bob 120 singularly, or by Alice 110 and Bob 120 incombination, and may be expanded to other WTRUs. As shown in FIG. 10, aslight difference between Eve's 130 channel observation and Bob120/Alice's 110 channel observation may result in a significantdifference in the error rate observed by Alice 110 relative to the errorrate observed by Eve 130. Thus, Alice 110 and Bob 120 can ensure thatEve 130 has the higher error rate by making only slight adjustments innoise or distortion levels. As a result, Alice 110 and Bob 120 canmaintain a quality communication, while limiting Eve's 130 ability tocompromise security sensitive information.

FIG. 11 is an example of a JRNSO procedure performed by the system ofFIG. 1. In this example, a loop back approach is used in a Time DivisionDuplex (TDD) mode using private pilots and private gain functions knownonly to the respective sender, Alice 110 or Bob 120.

The JRNSO process starts when Alice 110 modifies a private pilot p_(A)1100 with a private gain function G_(A) 1103, creating a signalG_(A)p_(A) 1106. Then, Alice 110 transmits the signal G_(A)p_(A) 1106 toBob 120 over channel G 1109, creating the resulting signal GG_(A)p_(A)1112. Bob 120 receives the signal GG_(A)p_(A) 1112 and translates thesignal to baseband. Then, Bob 120 modifies the signal GG_(A)p_(A) 1112with a private gain function G_(B) 1115, creating a resulting signalG_(B)GG_(A)p_(A) 1118. Bob 120 sends the signal G_(B)GG_(A)p_(A) 1118back to Alice 110 over the same channel G 1109, which creates aresulting signal GG_(B)GG_(A)p_(A) 1121. Then, Alice 110 receives thelooped back signal GG_(B)GG_(A)p_(A) at 1124 completing her loop backprocess during the JRNSO period.

Bob 120 starts his loop back process when he modifies a private pilotp_(B) 1130 with a private gain function G_(B) 1115, creating a signalG_(B)p_(B) 1133. Then, Bob 120 transmits the signal G_(B)p_(B) 1133 toAlice 110 over channel G 1109, creating the resulting signal GG_(B)p_(B)1136. Alice 110 receives the signal GG_(B)p_(B) 1136 and translates thesignal to baseband. Then, Alice 110 modifies the signal GG_(B)p_(B) 1136with a private gain function G_(A) 1103, creating a resulting signalG_(A)GG_(B)p_(B) 1139. Bob 120 sends the signal G_(A)GG_(B)p_(B) 1139back to Bob 120 over the same channel G 1109, which creates a resultingsignal GG_(A)GG_(B)p_(B) 1142. Then, Bob 120 receives the looped backsignal GG_(A)GG_(B)p_(B) at 1145 completing his loop back process duringthe JRNSO period.

During the JRNSO communication between Alice 110 and Bob 120, Eve 130may monitor Alice's 110 transmitted signals over channel G_(AE) 1151 andBob's 120 transmitted signals over channel G_(BE) 1154. If Eve 130 ismonitoring Alice's 110 transmissions, Eve 130 observes the signalsG_(AE)G_(A)p_(A) 1157 and G_(BE)G_(B)GG_(A)p_(A) 1160. If Eve 130 ismonitoring Bob's 120 transmissions, Eve 130 observes the signalsG_(BE)G_(B)p_(B) 1163 and G_(AE)G_(A)GG_(B)p_(B) 1166.

After the loop back process has been completed for Alice 110 and Bob120, then Alice 110 has observed GG_(B)GG_(A)p_(A) 1121 and GG_(B)p_(B)1136; and Bob 120 has observed GG_(A)p_(A) 1112 and GG_(A)GG_(B)p_(B)1142. Because Alice 110 and Bob 120 respectively, know the privatepilots and private gain functions they used, Alice 110 can process herlooped back signal GG_(B)GG_(A)p_(A) 1121 to determine the channelmatrix GG_(B)GG_(A). Bob 120 can process his looped back signalGG_(A)GG_(B)p_(B) 1142 to determine the channel matrix GG_(A)GG_(B). Inthis example, Alice 110 and Bob 120 use single-input-single-output(SISO) channels. The channel matrices are Rank 1, degenerate to a singlevalue, and are commutative (e.g. G_(AB)G_(BA)=G_(BA)G_(AB)). Using thecommutative properties of the channel matrices, Alice 110 and Bob 120determine essentially identical CIRs.

Eve 130 has observed G_(AE)G_(A)p_(A) 1157, G_(AE)G_(A)GG_(B)p_(B) 1166,GB_(E)G_(B)GG_(A)p_(A) 1160, and GB_(E)G_(B)p_(B) 1163. However, due tothe private nature of the pilots in this example, Eve 130 is unable toseparate the channel induced scaling, skewing, and rotational effectsfrom the settings inherent to the pilots. Therefore, Eve 130 is unableto determine G_(BA)G_(AB) even if Eve 130 has unlimited computationalabilities.

FIG. 12 shows an example of a time function example of the signalingprocess shown in FIG. 11. There is one reciprocal channel G 1109 overwhich Alice 110 and Bob 120 transmit and receive signals. There is atime period (k) 1200, which is the minimum required correlation timebetween Alice 110 and Bob 120. Since both Alice 110 and Bob's 120measurements are being made sequentially utilizing the same channel, itmust remain sufficiently correlated to experience essentially the samechannel effects for all of the measurement time periods. The channeleffects are scaling, skewing, and rotational changes to the amplitude,frequency, and phase settings inherent to the private pilots. Theminimum required correlation time 1200 consists of Alice's 110 JRNSOdetermination period 1205 and Bob's 120 JRNSO determination period 1210.There is a data period (k−1) 1215 which proceeds the JRNSO period (k)1200. There is a data period (k+1) 1220 which occurs subsequent to theJRNSO period (k) 1200. All G's are functions of the time periods.

Alice 110 initiates her loop back process by transmitting a signal at1225 to Bob 120 over channel G 1109, the resulting signal beingGG_(A)p_(A) 1225, where p_(A) is a private pilot known only to Alice110, and G_(A) is a private gain function known only to Alice 110 and isused to modify pA. Bob 120 then receives the signal, translates thesignal to baseband, applies a private gain function G_(B) known only toBob 120, converts the signal back to the carrier, and sends the signalback to Alice 110 over the same channel G 1109. Alice 110 then receivesthe looped back signal GG_(B)GG_(A)p_(A) at 1230, completing her loopback process.

Next, Bob 120 initiates his loop back process by transmitting a signalto Alice 110 over channel G 1109, the resulting signal being GG_(B)p_(B)1235, where G is a function of time, p_(B) is a private pilot known onlyto Bob 120, and G_(B) is a private gain function known only to Bob 120and is used to modify p_(B). Alice 110 translates the signal tobaseband, applies a private gain function G_(A) known only to Alice,converts the signal back to the carrier, and sends the signal back toBob 120 over the same channel G 1109. Bob 120 then receives the loopedback signal GG_(A)GG_(B)p_(B) at 1240, completing his loop back process.

In this example, the minimum required correlation time 1200 is achievedwhen Alice 110 initiates and completes her loop back process, and thenBob 120 initiates and completes his loop back process. Thus, thechannels must be correlated after four transmissions are sent. Alice 110and Bob 120 may reduce the minimum required correlation time by pairingtogether like transmissions in order to reduce the number oftransmissions required to perform channel measurements.

It should be noted that if Eve 130 algebraically processes the samplesprior to statistical analysis, then Alice 110 and Bob 120 may use themethods discussed in the FDD section to prevent synchronization, and toexploit their greater signal to noise ratio.

FIG. 13 is a time function example of the signaling process shown inFIG. 11, here showing pilot usage with paired like transmissions. Thereis one reciprocal channel G 1109 between Alice 110 and Bob 120 overwhich all signals are transmitted and received. There is a time period(k) 1300, which represents JRNSO usage of the channel G 1109 betweenAlice 110 and Bob 120. There are two minimum correlation time periodsdepicted at 1305 and 1310. There is a data period (k−1) 1315 whichproceeds the JRNSO period (k) 1300. There is a data period (k+1) 1320which occurs subsequent to the JRNSO period (k) 1300. All G's arefunctions of the time periods.

Pilot sequences are broken into blocks and transmitted by Alice 110 andBob 120 in alternating succession, called a paired transmission.Similarly, return signals are broken into blocks and transmitted byAlice 110 and Bob 120 in alternating succession, also called a pairedtransmission. One paired transmission 1305 consists of Alice's 110 pilottransmission, as depicted at 1325, and Bob's 120 pilot transmission, asdepicted at 1330. Another paired transmission 1310 consists of Alice's110 loop back transmission, as depicted at 1335, and Bob's 120 loopbacktransmission, as depicted at 1340.

Alice 110 starts the process at 1325 by transmitting a signal to Bob 120over channel G 1109, the resulting signal being GG_(A)p_(A), where p_(A)is a private pilot known only to Alice 110, and G_(A) is a private gainfunction known only to Alice 110 and used to modify p_(A). Then, Bob 120receives the signal GG_(A)p_(A). Then, Bob 120 transmits a differentsignal to Alice 110 over channel G 1109, the resulting signal beingGG_(B)p_(B), where p_(B) is a private pilot known only to Bob 120, andG_(B) is a private gain function known only to Bob 120 and used tomodify p_(B). Then Alice 110 receives the signal GG_(B)p_(B). To thispoint, there have been two transmissions: one pilot transmission byAlice 110, and one pilot transmission by Bob 120.

Bob 120 then transmits Alice's 110 return signal to Alice 110 multipliedby his private gain function G_(B). Alice 110 then receives her loopedback signal. Then Alice 110 transmits Bob's 120 looped back signal toBob 120 multiplied by his private gain function G_(A) and Bob 120receives the signal. At this point, there have been a total of fourtransmissions: two by Alice 110 and two by Bob 120.

In summary, this approach has the outbound initial transmission fromeach terminus sequentially performed first, and the received signalsstored at the loop back terminus The loop back terminuses thensequentially take their stored baseband signals, multiply them by theirown private gain function and send them back to the initiators. Sinceeach knows the private pilot they initially sent, they determine theassociated matrix product: GG_(B)GG_(A) for Alice and GG_(A)GG_(B) forBob.

Thus, as demonstrated by the example in FIG. 13, pairing transmissionstypes in TDD mode significantly reduces the channel correlation time forAlice 110 and Bob 120 to make their measurement.

In the example of FIG. 13, the paired transmissions may be identitymatrices or complex matrices which vary as a function of time. Morecomplex matrices generally result in greater JRNSO security.Additionally, Alice 110 and Bob 120 may use non-identity values for theprivate gain functions during the data periods to hide the JRNSO periodvalues. The non-identity values may be derived by pre-processing thedata streams to compensate for measured channel distortions.

FIG. 14 shows an example of signal flow during a pilot period in TDDmode using public pilots and private gain functions. In this example,private pilots are not used and there is no looped back signal. There isone channel G 1109 over which Alice 110 and Bob 120 transmit and receivesignals.

If Alice 110 is the transmitting terminus, then at 1405, Alice 110modifies a public pilot p with a private gain function G_(A), whereG_(A) is known only to Alice 110. At 1410, Alice 110 transmits thesignal G_(A)p over channel G 1109 to Bob 120, creating the resultingsignal GG_(A)p. At 1415, Bob 120 receives the signal GG_(A)p, translatesthe signal to baseband at 1420, and multiplies the baseband signal witha private gain function G_(B) at 1425, where G_(B) is known only to Bob120. Assuming derivation of the channel product is order insensitive(e.g. SISO and therefore commutative), Bob 120 may multiply the signalwith the private gain function G_(B) before or after Bob 120 determinesthe channel matrix product. If Bob 120 determines the channel productGG_(A) first, then multiplies that product by his private gain functionG_(B), the resulting matrix is G_(B)GG_(A). If Bob 120 applies his gainfunction G_(B) first, then determines the channel product, the resultingmatrix is GG_(A)G_(B). Under either scenario, Bob 120 uses the channelproduct GG_(A) for symbol recovery and the channel products, G_(B)GG_(A)or GG_(A)G_(B), for JRNSO information.

If Bob 120 is the transmitter, then at 1430, Bob 120 modifies a publicpilot p with a private gain function G_(B), where G_(B) is known only toBob 120. At 1435, Bob 120 transmits the signal G_(B)p over channel G1109 to Alice 110, creating the resulting signal GG_(B)p. At 1440, Alice110 receives the signal GG_(A)p, translates the signal to baseband at1445, and multiplies the baseband signal with a private gain functionG_(A) at 1450, where G_(B) is known only to Alice 110. Assumingderivation of the channel product is order insensitive (e.g. SISO andtherefore commutative), Alice 110 may multiply the signal with theprivate gain function G_(B) before or after Alice 110 determines thechannel matrix product. If Alice 110 determines the channel productGG_(B) first, then multiplies that product by her private gain functionG_(A), the resulting matrix is G_(A)GG_(B). If Alice 110 applies hergain function G_(A) first, then determines the channel product, theresulting matrix is GG_(A)G_(B). Under either scenario, Alice 110 usesthe channel product GG_(B) for symbol recovery and the channel products,G_(A)GG_(B) or GG_(B)G_(A), for JRNSO information.

During the communication, Eve 130 may monitor Alice's 110 transmissionover channel G_(AE) 1455 and Bob's 120 transmission over channel G_(BE)1460. If Eve 130 is monitoring Alice's 110 transmission, Eve 130observes G_(AE)G_(A)p. If Eve 130 is monitoring Bob's 120 transmission,Eve 130 observes G_(BE)G_(B)p. Because Eve 130 knows the public pilot p,Eve 130 may process the observed signals at 1465, 1470 to determine thechannel products G_(AE)G_(A) and G_(BE)G_(B). While Eve 130 may use thechannel products for symbol recovery, Eve 130 does not know the privatefunctions G_(A) and G_(B). Therefore, Eve 130 is unable to determineAlice's 110 and Bob's 120 JRNSO information.

In the example of FIG. 14, the same private gain function values usedduring the JRNSO period may also be used during the data period. Thechannel and private gain products derived from the pilots can be usedfor data processing.

FIG. 15 shows an example of signal flow during a data period in TDD modeusing public pilots and private gain functions. There is one channel G1109 over which Alice 110 and Bob 120 transmit and receive signals.

If Alice 110 is transmitting, then at 1505, Alice 110 multiplies a datasymbol d_(A) with a private gain function G_(A), where G_(A) is knownonly to Alice 110. At 1510, Alice 110 sends the signal G_(A)d_(A) overchannel G 1109 to Bob 120, creating the resulting signal GG_(A)d_(A).Bob 120 receives the signal GG_(A)d_(A) at 1515. At 1520, Bob 120processes the signal to baseband. At 1525, Bob 120 further processes thesignal and extracts d_(A) and GG_(A), where d_(A) is used as data 1530,and GG_(A) is stored for optional JRNSO use 1535.

If Bob 120 is transmitting, then at 1537, Bob 120 multiplies a datasymbol d_(B) with a private gain function G_(B), where G_(B) is knownonly to Bob 120. At 1540, Bob 120 sends the signal G_(B)d_(B) overchannel G 1109 to Alice 110, creating the resulting signal GG_(B)D_(B).Alice 110 receives the signal GG_(B)D_(B) at 1545. At 1550, Alice 110processes the signal to baseband. At 1555, Alice 110 further processesthe signal and extracts d_(B) and GG_(B), where d_(B) is used as data,and GG_(B) is stored for optional JRNSO use.

Eve 130 may monitor Alice's 110 transmissions over channel G_(AE) 1565,and Bob's 120 transmissions over channel G_(BE) 1570. If Eve 130monitors Alice's 110 transmission, Eve 130 observes G_(AE)G_(A)d_(A). At1575, Eve 130 may further process Alice's signal to extract d_(A) andG_(AE)G_(A). If Eve 130 monitors Bob's 120 transmission, Eve 130observes G_(BE)G_(B)d_(B). At 1580, Eve 130 further processes Bob's 120signal to extract d_(B) and G_(BE)G_(B). However, because Eve 130 doesnot know the private gain functions G_(A) and G_(B), Eve 130 is unableto determine the JRNSO information, as shown at 1585. FIG. 16 shows anexample of a Kalman filter using pilots and data to decode symbols. Thechannel estimate 1600 is a value set, or subset, recorded at the end ofeach channel pairing measurement period.

FIG. 17 shows an example of Kalman filtering time directionalprocessing. Data is processed in reverse time order to improvecomparison of mutually determined value sets. Alice 110 uses the values1600 to determine JRNSO information corresponding to Bob's 120 pairedmeasurement, and vice versa. Optimally, the Alice 110 and Bob 120process the Kalman filter output as close as possible to the transitionboundary between the JRNSO periods and the data periods. As shown at1705, Alice 110 and Bob 120 process the same data in both the forwardand reverse time direction. The reverse time seeding is the last channelset which is calculated from the forward time calculation. Optimally,the symbols in the forward direction are exploited in the reversedirection. Alternatively, the seeding is derived from the priormeasurement period if forward time processing is not required in thepresent time period. The prior measurement period in the latter examplecould be forward or reverse in time.

Alternatively, Alice's 110 and Bob's 120 statistical determination ofthe channel information is biased toward the JRNSO period-data periodtransition boundary using sliding windows or weighted samples.

It should be noted that for simplicity, the above embodiments weredescribed in single-input-single-output (SISO) orsingle-input-multiple-output SIMO) mode. In fact, the JRNSO applicationsin FDD and TDD may also be used in multiple-input-multiple-out (MIMO) ormultiple-input-single-output (MISO) modes. The following MIMOembodiments are described where Alice 110 and Bob 120 each have twoantenna elements. In fact, Alice 110 and Bob 120 may have more than twoantenna elements. Additionally, Alice 110 and Bob 120 may have differentnumbers of antenna elements. Array couplings, dimensional antennapatterns and polarizations may be used in place of distinct antennaelements. Optimally, channel paths between Alice 110 and Bob 120 areused in parallel during the propagation time periods so that each loopback channel pair is measured as close in time as possible.Alternatively, channel paths between Alice 110 and Bob 120 are usedsequentially during the propagation periods to reduce the effects ofinterference. Optimally, Alice 110 and Bob 120 use the minimum number ofantenna elements required to protect JRNSO secrecy.

FIG. 18 is an example of a block diagram showing a loop back signal flowusing the fewest time periods for MIMO RF networks. Signal flow duringAlice's 110 loop back cycle is shown at 1800. Signal flow during Bob's120 loop back cycle is shown at 1805. There are three time periods shownfor Alice's 110 loop back process and three time periods shown for Bob's120 loop back process. Time periods are depicted in pairs. Initialtransmissions (primary) are sent at time period 1. Looped back signalsare transmitted at time periods 2 and 3. If Alice 110 is the initialtransmitter, Alice 110 transmits a signal from one antenna element, Bob120 receives the signal over two antenna elements, then Bob 120 returnstwo signals to Alice 110 sequentially from one antenna element. Alice110 then receives the looped back signal over two antenna elements.

For Alice's 110 loop back process 1800, at time period 1 1810, Alice 110transmits a pilot signal from antenna element A1 1815 and Bob 120receives the signal over antenna elements B1 1820 and B2 1825. At timeperiod 2 1930, Bob 120 sends a return signal from antenna element B11820 and Alice 110 receives the looped back signal over antenna elementsA1 1815 and A2 1840. At time period 3 1835, Bob 120 transmits a signalfrom antenna element B2 1825 to antenna element B1 1820, and thentransmits the signal from antenna element B1 1820 to Alice 110. Stillshown at time period 3 1835, Alice 110 receives the looped back signalover antenna elements A1 1815 and A2 1840. Alice 110 receives no loopedback signals directly from Bob's 120 antenna element B2 1825.

For Bob's 120 loop back process 1805, at time period 1 1845, Bob 120transmits a pilot signal from antenna element B1 1850 and Alice 110receives the signal over antenna elements A1 1855 and A2 1860. At timeperiod 2 1865, Alice 110 sends a return signal from antenna element A11855 and Bob 120 receives the looped back signal over antenna elementsB1 1850 and B2 1870. At time period 3 1875, Alice 110 transmits a signalfrom antenna element A2 1860 to antenna element A1 1855, and thentransmits the signal from antenna element A1 1855 to Alice 110. Stillshown at time period 3 1875, Bob 120 receives the looped back signalover antenna elements B1 1850 and B2 1870. Bob 120 receives no loopedback signals directly from Alice's 110 antenna element A2 1860.

After Alice 110 has completed her loop back process 1800, Alice 110 hasobserved two signals over antenna element A1 1815: one signalJ_(B1A1)J_(A1B1)p_(A1) during time period 2 1830, and another signalJ_(B1A1)J_(A1B2)p_(A1) during time period 3 1835. Alice 110 has alsoobserved two signals over antenna element A2 1940: one signalJ_(B1A2)J_(A1B1)p_(A1) during time period 2 and another signalJ_(B1A2)J_(A1B2)p_(A1) during time period 3.

After Bob 120 has completed his loop back process, Bob 120 has observedtwo signals over antenna element B1 1945: one signalJ_(A1B1)J_(B1A1)p_(B1) during time period 2, and another signalJ_(A1B1)J_(B1A2)p_(B1). Bob 120 has also observed two signals overantenna element B2 1950: one signal J_(A1B2)J_(B1A1)p_(B1) during timeperiod 2, and another signal J_(A1B2)J_(B1A2)p_(B1) during time period3.

As shown in FIG. 18, after both Alice 110 and Bob 120 have completedtheir loop back cycles, Alice 110 and Bob 120 may correlate theirobserved channel products to determine essentially the same CIR.

In one embodiment, a non-SIMO or non-SISO array is reduced to SISO byusing one antenna at each terminus, where the antenna elements usedduring each successive loop back are identical.

In another embodiment, a non-SIMO or non-SISO case is reduced tomultiple instances of SISO or SIMO in order to increase the amount ofavailable CIR information. Signals are transmitted from a single antennaelement but received at multiple receive antenna elements. In thisembodiment, the receiving terminus activates its antenna elementssequentially when transmitting the loop back signals. The antennaelements used in each loop back cycle are identically paired so thatAlice 110 and Bob 120 may determine essentially the same CIR.

In another embodiment, MIMO is reduced to SIMO. At the transmittingterminus, one transmitting antenna element is activated to send signals.At the receiving terminus, signals are received over multiple antennaelements. The receiving terminus then sends the return signals back. Thereturn signals are received and decoded by the same transmissionelement. The process is repeated at each terminus so that Alice 110 andBob 120 are analyzing essentially identical commutative channelproducts.

FIG. 19 is an example of block diagram showing a loop back signal flowusing all unique signaling path segments in MIMO RF networks. Signalflow during Alice's 110 loop back process is depicted at 1900. Signalflow during Bob's 120 loop back process is depicted at 1903. There aresix time periods depicted for Alice's 110 loop back process and six timeperiods depicted for Bob's 120 loop back process. Time periods aredepicted in pairs. Initial transmissions (primary) are sent at timeperiod 1 and time period 4. Looped back signals are transmitted at timeperiods 2, 3, 5 and 6.

For Alice's 110 loop back process 1900, at time period 1, Alice 110transmits a pilot signal from antenna element A1 1906 and Bob 120receives the signal over antenna elements B1 1909 and B2 1912. At timeperiod 2, Bob 120 sends a return signal from antenna element B1 1909 andAlice 110 receives the looped back signal over antenna element A1 1906.At time period 3, Bob 120 transmits a return signal from antenna elementB2 1912 and Alice 110 receives the looped back signal over antennaelement A1 1906. At time period 4, Alice 110 transmits a pilot signalfrom antenna element A2 1915 and Bob 120 receives the signal overantenna elements B1 1918 and B2 1921. At time period 5, Bobs 120 sends areturn signal from antenna element B1 1918 and Alice 110 receives thelooped back signal at antenna element A2 1915. At time period 6, Bob 120sends a return signal from antenna element B2 1921 and Alice 110receives the looped back signal over antenna element A2 2015.

For Bob's 120 loop back process, at time period 1, Bob 120 transmits apilot signal from antenna element B1 1924 and Alice 110 receives thesignal over antenna elements A1 1927 and B2 1930. At time period 2,Alice 110 sends a return signal from antenna element A1 1927 and Bob 120receives the looped back signal over antenna element B1 1924. At timeperiod 3, Alice 110 transmits a return signal from antenna element A21930 and Bob 120 receives the looped back signal over antenna element B11924. At time period 4, Bob 120 transmits a pilot signal from antennaelement B2 1933 and Alice 110 receives the signal over antenna elementsA1 1936 and A2 1939. At time period 5, Alice 110 sends a return signalfrom antenna element A1 1936 and Bob 120 receives the looped back signalat antenna element B2 1933. At time period 6, Alice 110 sends a returnsignal from antenna element A2 1939 and Bob 120 receives the looped backsignal over antenna element B2 1933.

After Bob and Alice complete their loop back cycles, they may correlatetheir received channel product data as shown in FIG. 19.

FIG. 20 is a table showing all possible propagation products where Alice110 and Bob 120 each have two antenna elements. Alice's 110 antennaelements are designated A1 and A2. Bob's 120 antenna elements aredesignated B1 and B2. Primary transmissions are shown by reference 1 (A1and B1) and reference 6 (A2 and B2). Loop back transmissions of theprimary signal of reference 1 are shown at references 2, 3, 4, and 5.Loop back transmissions of the primary signal of reference 6 are shownby references 7, 8, 9, and 10. As shown in FIG. 20, there are thirty-twopropagation products of the looped back signals in a 2×2 MIMOconfiguration. After Alice 110 and Bob 120 complete their loop backprocess, Alice 110 has observed sixteen propagation products, and Bob120 has observed sixteen propagation products. As shown, Alice 110 cancorrelate her sixteen propagation products with Bob's sixteenpropagation products.

FIG. 21 is a time function example of JRNSO subset measurement usage inMIMO RF networks. Time increases from left to right. As demonstrated,data exchange periods alternate with JRNSO periods. The JRNSO periodsare designated as JRNSO subset usage (k−1) 2105, JNSRO subset usage (k)2110, and JRNSO subset usage (k+1) 2115.

FIG. 22 is an example of a block diagram showing signal flow in FDD MIMOmode using private pilots and private gain functions. Symmetricfunctions of MIMO products are used to calculate channel transforms.

Alice's 120 loop back process begins at 2203 when Alice 110 multiplies aprivate pilot p_(A) with a gain function G_(A), where p_(A) and G_(A)are known only to Alice At 2206, Alice 110 transmits the signalG_(A)p_(A) over channel G_(AB) 2209 to Bob 120, creating the resultingsignal G_(AB)G_(A)p_(A). Bob 120 receives the signal at 2212, translatesthe signal to baseband at 2215, multiplies the signal with gain functionG_(B) at 2218, and at 2221, transmits the signal over a channel with adifferent frequency G_(BA) 2224, creating resulting signalG_(BA)G_(B)G_(AB)G_(A)p_(A). At 2227, Alice receives the signalG_(BA)G_(B)G_(AB)G_(A)p_(A).

Bob's 120 loop back process begins at 2218 when Bob 120 multiplies aprivate pilot p_(B) with a gain function G_(B), where p_(B) and G_(B)are known only to Bob 120. At 2222, Bob 120 transmits the signalG_(B)p_(B) over channel G_(BA) 2224 to Alice 110, creating the resultingsignal G_(BA)G_(B)p_(B). Alice 110 receives the signal at 2228,translates the signal to baseband at 2230, multiplies the signal withgain function G_(A) at 2203, and at 2207, transmits the signal over achannel with a different frequency G_(AB) 2209, creating the resultingsignal G_(AB)G_(A)G_(BA)G_(B)p_(B). At 2213, Bob 120 receives the signalG_(AB)G_(A)G_(BA)G_(B)p_(B).

After Alice 110 has completed her loop back process, Alice 110 hasobserved G_(BA)G_(B)G_(AB)G_(A)p_(A). At 2233, Alice 110 processes herprivate pilot p_(A) to determine G_(BA)G_(B)G_(AB)G_(A). After Bob 120has completed his loop back process, Bob 120 has observedG_(AB)G_(A)G_(BA)p_(B). At 2236, Bob 120 processes his private pilotp_(B) to determine G_(AB)G_(A)G_(BA)G_(B).

Eve 130 may monitor Alice's 110 transmissions over channel G_(AE) 2239and Bob's 120 transmissions over channel G_(BE) 2242. If Eve 130 ismonitoring Alice's 110 transmission, Eve 130 observes G_(AE)G_(A)p_(A)and G_(AE)G_(A)G_(BA)G_(B)p_(B). If Eve 130 is monitoring Bob's 120transmissions, Eve 130 observes G_(BE)G_(B)p_(B) andG_(BE)G_(B)G_(AB)G_(A)p_(A). However, because Eve 130 does not know theprivate pilots p_(A) and p_(B), Eve 130 cannot calculate the channeltransforms.

As further shown in the loop back example of FIG. 22, the channeltransforms used during the JRNSO periods differ from the channeltransforms used during the data periods. This is necessary because Eve130 can use the public pilot p to determine the channel transformsduring the data periods. In one embodiment, Eve 130 is prevented fromdetermining the channel transforms during the JRNSO period by making theswitch over time between data and JRNSO periods exceed the maximumcoherence time of the channels. The same concepts described previouslyfor SISO may be utilized in this scenario. Alternatively, the end to endchannel transforms are modified so that Eve cannot separate the channelmodification effects from the natural channel effects.

In the MIMO loop back example of FIG. 22, the channel transforms are notcommutative. However, instead of reducing MIMO cases to SISO or SIMO toderive JRSNO information from the CIR matrices, JRNSO may be derivedfrom special functions of the channel product matrices. These may beapplied to any MIMO or SISO case. In this embodiment symmetricfunctions, which determine results which are independent of the order ofchannel operations are utilized. The determinant and the trace of amatrix are examples of such functions. However, many other symmetricfunctions of matrices exist. Mathematically, the property ofdeterminants being exploited is described as,

det(J_(BA)J_(AB))=det(J_(AB))det(J_(BA)), where each entry in thematrices is singularly valued. Thus, the determinants are singularlyvalued and commutative, so that

det(J_(BA)J_(AB))=det(J_(AB))det(J_(BA))=det(J_(BA))(J_(AB))=det(J_(AB)J_(BA)),where an N×N function, which contains N independent shared values thatAlice 110 and Bob 120 can use to derive a common shared key, isconverted into a single value.

For a general definition of a symmetric function,

let X₁, . . . , X_(N) be a set of N arguments which is potentiallymatrix-valued. Then, a function f(X₁, . . . , X_(N)) is symmetric if itis invariant to the permutation of its arguments.

For example

p: [1, . . . , N] [1, . . . N] is a permutation on the set [1, . . . ,N]. Thus, a function f is symmetric for any such p if f(X_(p(1)), . . .X_(p(N)))=f(X₁, . . . X_(N)).

For processing the asymmetric round-trip matrices resulting in the MIMOand SISO cases, a specific family of symmetric functions known asSymmetric Principal Minor Sums (SPMSs) is used.

Let I, J, be k-element subsets of [1, . . . , N]. For an N×N matrix X,then

X _(I,J) ={x _(i,j) εX:iεI,jεJ}

where X_(I,J) is a k×k matrix whose elements are selected using theindex sets I and J. The [I, J]-minor of X is the determinant of X_(i,j),denoted by [X]_(I,J) A minor is a principal minor if I=J. The minorssatisfy the following property

$\lbrack{AB}\rbrack_{I,J} = {\sum\limits_{K}{\lbrack A\rbrack_{I,K}\lbrack B\rbrack}_{K,J}}$

where the sum is taken over all possible k-element subsets of [1, . . ., N] (denoted by K).

For an N×N matrix X, define N+1 elementary SPMSs (eSPMSs) as follows:

S ₀(X)=1.

For 1≦n≦N

${S_{n}(X)} = {\sum\limits_{I}\lbrack X\rbrack_{I,I}}$

where the sum is taken over all n-element subsets of [1, . . . , N].Such sums are symmetric in the matrix product, as demonstrated by

${S_{n}({AB})} = {{\sum\limits_{I}\lbrack{AB}\rbrack_{I,I}} = {{\sum\limits_{I}{\sum\limits_{K}{\lbrack A\rbrack_{I,K}\lbrack B\rbrack}_{K,I}}} = {{\sum\limits_{K}{\sum\limits_{I}{\lbrack B\rbrack_{K,I}\lbrack A\rbrack}_{I,K}}} = {{\sum\limits_{K}\lbrack{BA}\rbrack_{KK}} = {S_{n}({BA})}}}}}$

where the third equality follows by commuting the outer sums and theinner product.

The eSPMS functions form a “baseline set” for generating more complexsymmetric functions of minors. For example, any products or linearcombinations which are polynomials of eSPMSs are symmetric functions ofmatrix products.

Additionally, the eSPMS functions are related to the eigenvalues oftheir argument matrices. For example, let 1, . . . , n be the Neigenvalues of the N×N matrix X. Then,

${S_{n}(X)} = {\sum\limits_{1 \leq i_{1} < \mspace{11mu} \ldots \mspace{11mu} < i_{n} \leq N}{\lambda_{i_{1}} \times \ldots \times \lambda_{i_{n}}}}$

where the polynomials of eigenvalues on the right-hand side are the wellknown elementary symmetric polynomials in N variables, defined by

${E_{N,n}\left( {x_{1},\ldots \mspace{14mu},x_{n}} \right)} = {\sum\limits_{1 \leq i_{1} < \mspace{11mu} \ldots \mspace{11mu} < i_{n} \leq N}{x_{i_{1}} \times \ldots \times x_{i_{n}}}}$

Therefore, the elementary symmetric polynomials of eigenvalues of matrixproducts are invariant to the order in which matrices are multiplied,even through the eigenvalues or their products are not invariant to theorder of multiplication.

Note that the determinant of an N×N matrix X is just S_(N)(X) and thetrace N×N matrix X is just S₁(X). Therefore, SPMSs represent ageneralization of the notion of a matrix determinant and trace. Therelationship is established either from the minor-based definition ofSPSMs or the alternative, eigenvalue based definition.

In one embodiment, SPMS are computed based on the computation ofprincipal minors. Convergence is guaranteed but computation of principalminors may be complex.

In another embodiment, SPMS are computed based on eigenvalues.Eigenvalues are calculated in iterations which does not guaranteeconvergence. Therefore, eigenvalues are computed using low complexityapproximations.

In another embodiment, symmetric functions are determined using squarematrices where Alice 110 and Bob 120 have an unequal number of input andoutput streams. A subset which has equal dimensions is selected for eachJRNSO transmission and loop back. To increase the amount of mutuallyavailable JRNSO information, each unique square subset is used.

FIG. 23 is a table showing sample square transmission sequences.Signaling products with like terms are used to derive square matrices.The square matrices have symmetric functions which are equal within thenoise and variance limits over the measurement periods. Subscriptsindicate which transceiver element is being used. No subscripts indicatethat all transceiver elements are being used. Each path is used at leastonce to exhaust the available channel information and exploit the loopback products. Matrix row entries once used are not re-utilized.Alternatively, where the channels lack orthogonal characteristics, Alice110 and Bob 120 transmit signals over five time periods using time as anorthogonalizing factor. The numbering of antenna elements is arbitraryand changes the phase of eSPMS but not their absolute value.

It should be noted that Alice 110 and Bob 120 may protect their securityeven if it appears they are having legitimate communication with Eve130. During the communication with Eve 130, Alice 110 and Bob 120 useunique private gain functions. Alice 110 and Bob 120 continue to useunique private gain functions in communication with any other terminus

In situations where Alice 110 and Bob experience significant loop backpower loss, Alice 110 and Bob 120 may amplify the primary signal with again multiplier before the primary signal is looped back to its source.

FIG. 24 is an example of a block diagram of signal flow in FDD mode.Gain multipliers D_(X) are used to amplify the primary signal before theprimary signal is looped back to its source.

Alice's 110 loop back process begins at 2400 when Alice 110 multiplies aprivate pilot p_(A) by a private function G_(A). At 2403, Alice 110transmits the signal G_(A)p_(A) over channel G_(AB) 2406 to Bob 120,creating a resulting signal G_(AB)G_(A)p_(A). At 2409, Bob 120 receivesthe signal G_(AB)G_(A)p_(A) At 2412, Bob 120 translates the signal tobaseband. At 2415, Bob 120 amplifies the signal with a gain multiplierD_(B). At 2418, Bob 120 applies a private gain function G_(B) to thesignal. At 2421, Bob 120 transmits the signal G_(B)D_(B)G_(AB)G_(A)p_(A)to Alice 110 over a channel with a different frequency G_(BA) 2424,creating a resulting signal G_(BA)G_(B)D_(B)G_(AB)G_(A)p_(A). At 2427,Alice 110 receives the signal G_(BA)G_(B)D_(B)G_(AB)G_(A)p_(A).

Bob's 120 loop back process begins at 2418 when Bob 120 multiplies aprivate pilot p_(B) by a private function G_(B). At 2422, Bob 120transmits the signal G_(B)p_(B) over channel G_(BA) 2424 to Alice 110,creating a resulting signal G_(BA)G_(B)p_(B). At 2428, Alice 110receives the signal G_(BA)G_(B)p_(B). At 2430, Alice 110 translates thesignal to baseband. At 2433, Alice 110 amplifies the signal with a gainmultiplier D_(A). At 2400, Alice 110 applies a private gain functionG_(A) to the signal. At 2428, Alice 110 transmits the signalG_(A)D_(A)G_(AB)G_(B)p_(B) to Bob 120 over channel G_(AB) 2406, creatinga resulting signal G_(AB)G_(A)D_(A)G_(BA)G_(B)p_(B). At 2410, Bob 120receives the signal G_(AB)G_(A)D_(A)G_(BA)G_(B)p_(B).

After Alice has completed her loop back process, Alice 110 has observedG_(BA)G_(B)D_(B)G_(AB)G_(A)p_(A). At 2436, Alice 110 processes herprivate pilot p_(A) to determine G_(BA)G_(B)D_(B)G_(AB)G_(A). After Bob120 has completed his loop back process, Bob 120 has observedG_(AB)G_(A)D_(A)G_(BA)G_(B)p_(B). At 2439, Bob 120 processes his privatepilot p_(B) to determine G_(AB)G_(A)D_(A)G_(BA)G_(B).

Eve 130 may monitor Alice's 110 transmissions over channel G_(AE) 2442and Bob's 120 transmissions over channel G_(BE) 2445. If Eve 130 ismonitoring Alice's 110 transmissions, Eve 130 observes G_(AE)G_(A)p_(A)and G_(AE)G_(A)D_(A)G_(BA)G_(B)p_(B). If Eve 130 is monitoring Bob's 120transmissions, Eve 130 observes G_(BE)G_(B)p_(B) andG_(BE)G_(B)D_(B)G_(AB)G_(A)p_(A). Because Eve 130 does not know eitherpilot p_(A) or p_(B), Eve 130 is unable to calculate the channeltransforms. As in similar examples, the switch over delay exceeds themaximum channel coherence time.

In this embodiment, information is extracted by selecting the relativecomplex vector rotations values of the eSPMS. For example, the complexvector rotation values may be the angular rotation, or the Input Phaseto Quadrature Phase amplitude ratio. Because the gain multipliers arereal valued diagonal matrices, each received stream may be multiplied bya different compensating gain value. Alternatively, a single averagedgain value may be used to amplify each received stream to reduce theproduct of all the received streams to a single value. In the case of asingle gain for all signals, relative received power levels may beexploited. In the case of different path compensating gains, therelative gain loss between the paths can not be exploited.

Although features and elements are described above in particularcombinations, each feature or element can be used alone without theother features and elements or in various combinations with or withoutother features and elements. The methods or flow charts provided hereinmay be implemented in a computer program, software, or firmwareincorporated in a computer-readable storage medium for execution by ageneral purpose computer or a processor. The above embodiments, whichare discussed relative to FDD mode, also apply to TDD mode. Examples ofcomputer-readable storage mediums include a read only memory (ROM), arandom access memory (RAM), a register, cache memory, semiconductormemory devices, magnetic media such as internal hard disks and removabledisks, magneto-optical media, and optical media such as CD-ROM disks,and digital versatile disks (DVDs).

Suitable processors include, by way of example, a general purposeprocessor, a special purpose processor, a conventional processor, adigital signal processor (DSP), a plurality of microprocessors, one ormore microprocessors in association with a DSP core, a controller, amicrocontroller, Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs) circuits, any other type of integratedcircuit (IC), and/or a state machine.

A processor in association with software may be used to implement aradio frequency transceiver for use in a wireless transmit receive unit(WTRU), user equipment (UE), terminal, base station, radio networkcontroller (RNC), or any host computer. The WTRU may be used inconjunction with modules, implemented in hardware and/or software, suchas a camera, a video camera module, a videophone, a speakerphone, avibration device, a speaker, a microphone, a television transceiver, ahands free headset, a keyboard, a Bluetooth® module, a frequencymodulated (FM) radio unit, a liquid crystal display (LCD) display unit,an organic light-emitting diode (OLED) display unit, a digital musicplayer, a media player, a video game player module, an Internet browser,and/or any wireless local area network (WLAN) or Ultra Wide Band (UWB)module.

What is claimed is:
 1. A method for determining Joint Randomness NotShared by Others (JRNSO) comprising: transmitting, from a first wirelesstransmit/receive unit (WTRU) to a second WTRU over a first channelfrequency, a first signal comprising a first pilot; receiving, at thefirst WTRU from the second WTRU over a second channel frequency, asecond signal comprising a second pilot and a second channel effect,wherein the second channel frequency is different than the first channelfrequency; transmitting, from the first WTRU to the second WTRU over thefirst channel frequency, a third signal comprising the second signal;receiving, at the first WTRU from the second WTRU over the secondchannel frequency, a fourth signal comprising the first signal, a firstchannel effect, and the second channel effect; processing, at the firstWTRU, the fourth signal to determine overall channel effects; anddetermining, at the first WTRU, JRNSO based on the overall channeleffects.
 2. The method of claim 1 wherein the first pilot is a firstprivate pilot sequence and the second pilot is a second private pilotsequence.
 3. The method of claim 1 wherein the first signal comprises afirst private gain function effect and the second signal comprises asecond private gain function effect.
 4. The method of claim 3 whereinthe third signal comprises a first private gain function, and whereinthe fourth signal comprises a second private gain function and ismultiplied by the first private gain function upon its reception.
 5. Themethod of claim 1 wherein the first pilot is a public pilot.
 6. Themethod of claim 1 further comprising introducing false modulation intothe first signal and the third signal.
 7. The method of claim 6 whereinthe false modulation is introduced after receiving the fourth signal. 8.The method of claim 1 further comprising controlling a signal to noiseratio over a channel.
 9. The method of claim 1 wherein the second signaland the fourth signal are each received over a first receive element andat least one second receive element of the first WTRU.
 10. The method ofclaim 1 wherein the first signal and the third signal are eachtransmitted over a first transmit element and at least one secondtransmit element of the first WTRU.
 11. A wireless transmit/receive unit(WTRU) configured to determine Joint Randomness Not Shared by Others(JRNSO) comprising: a transmitter configured to transmit: a first signalcomprising a first pilot to a second WTRU over a first channelfrequency; and a third signal comprising a second signal to the secondWTRU over the first channel frequency; a receiver configured to receive:the second signal comprising a second pilot and a second channel effectfrom the second WTRU over a second channel frequency, wherein the secondchannel frequency is different than the first channel frequency; and afourth signal comprising the first signal, a first channel effect, andthe second channel effect from the second WTRU over the second channelfrequency; and a processor configured to: process the fourth signal todetermine overall channel effects; and determine JRNSO based on theoverall channel effects
 12. The WTRU of claim 11 wherein the first pilotis a first private pilot sequence and the second pilot is a secondprivate pilot sequence.
 13. The WTRU of claim 11 wherein the firstsignal comprises a first private gain function effect and the secondsignal comprises a second private gain function effect.
 14. The WTRU ofclaim 13 wherein the third signal comprises a first private gainfunction, and wherein the fourth signal comprises a second private gainfunction and is multiplied by the first private gain function upon itsreception.
 15. The WTRU of claim 11 wherein the first pilot is a publicpilot.
 16. The WTRU of claim 11 wherein the transmitter is furtherconfigured to introduce false modulation into the first signal and thethird signal.
 17. The WTRU of claim 16 wherein the false modulation isintroduced after receiving the fourth signal.
 18. The WTRU of claim 11the processor is further configured to control a signal to noise ratioover a channel.
 19. The WTRU of claim 11 wherein the second signal andthe fourth signal are each received over a first receive element and atleast one second receive element of the receiver.
 20. The WTRU of claim11 wherein the first signal and the third signal are each transmittedover a first transmit element and at least one second transmit elementof the transmitter.